Unicyclic graphs of given girth <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>k</mml:mi><mml:mo>≥</mml:mo><mml:mn>4</mml:mn></mml:math> having smallest general sum-connectivity index

Tomescu, Ioan; Kanwal, Salma

doi:10.1016/j.dam.2013.09.019

Cited by 16 publications

(5 citation statements)

References 13 publications

(20 reference statements)

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“…In [15], thegeneralized prism network of SK indices was investigated. In [16], Harisha et al calculated the SK indices of the semi-total point graph R(G) and subdivision graph S(G) on tetracenic nanotubes and tetracenicnanotori, two significant chemical structures. In [17], the behaviors of SK indices were investigated under some graph operations when defined on weighted and interval weighted graphs.…”

Section: Background Survey and Preliminary Resultsmentioning

confidence: 99%

Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

et al. 2023

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For a graph, the SK index is equal to the half of the sum of the degrees of the vertices, the SK1 index is equal to the half of the product of the degrees of the vertices, and the SK2 index is equal to the half of the square of the sum of the degrees of the vertices. This paper shows a simple and unified approach to the greatest SK indices for unicyclic graphs by using some transformations and characterizes these graphs with the first, second, and third SK indices having order r ≥ 5 and girth g ≥ 3, where girth is the length of the shortest cycle in a graph.

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Section: Background Survey and Preliminary Resultsmentioning

confidence: 99%

Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

et al. 2023

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“…Several extremal properties of the general sum-connectivity index have already been established for general graphs [8], multigraphs [6], trees [6,7,9], unicyclic graphs [10,11] and bicyclic graphs [12].…”

Section: Introductionmentioning

confidence: 99%

On the general sum-connectivity index of tricyclic graphs

Zhu

2015

J. Appl. Math. Comput.

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“…e Randić index was defined in 1975 [7]; later on the idea was subsequently extended to the generalized Randić connectivity index by Li and Gutman, see [8]. For more studies, we refer to [9][10][11][12].…”

Section: Introductionmentioning

confidence: 99%

Bounds of Degree-Based Molecular Descriptors for Generalized $F$ -sum Graphs

Liu

Akram

Javaid

et al. 2021

Discrete Dynamics in Nature and Society

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A molecular descriptor is a mathematical measure that associates a molecular graph with some real numbers and predicts the various biological, chemical, and structural properties of the underlying molecular graph. Wiener (1947) and Trinjastic and Gutman (1972) used molecular descriptors to find the boiling point of paraffin and total π -electron energy of the molecules, respectively. For molecular graphs, the general sum-connectivity and general Randić are well-studied fundamental topological indices (TIs) which are considered as degree-based molecular descriptors. In this paper, we obtain the bounds of the aforesaid TIs for the generalized F -sum graphs. The foresaid TIs are also obtained for some particular classes of the generalized F -sum graphs as the consequences of the obtained results. At the end, 3 D -graphical presentations are also included to illustrate the results for better understanding.

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Unicyclic graphs of given girth k≥4 having smallest general sum-connectivity index

Cited by 16 publications

References 13 publications

Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

On the general sum-connectivity index of tricyclic graphs

Bounds of Degree-Based Molecular Descriptors for Generalized $F$ -sum Graphs

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Unicyclic graphs of given girth k≥4 having smallest general sum-connectivity index

Cited by 16 publications

References 13 publications

Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

On the general sum-connectivity index of tricyclic graphs

Bounds of Degree-Based Molecular Descriptors for Generalized F -sum Graphs

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Bounds of Degree-Based Molecular Descriptors for Generalized $F$ -sum Graphs